There's a lot of talk in Lucy about humans only using 10% of their brain. This is an oft-repeated myth that drives scientists up a wall, but I'd like to believe it's a coded message from Luc Besson. Please, for your own sake, he implores, don't think too much about this movie. Instead, soak up Scarlett Johansson in a white T-shirt and black bra, making quizzical faces while despatching bad guys with the power of her mind and a few curt words in that trademark husky voice. As the techno soundtrack thrums and ScoJo cranks out lines like “the infinite components of the cell's nucleus is exploding inside my brain” many may recognize that this style of pseudo-intellectual action cinema is a type of drug, and, once in a while, you need a hit.

Johansson (despite being 29) plays an American student living in Taipei. Some sketchy dude she just started dating wants her to bring a locked briefcase to a mysterious Mr Keng (Choi Min-sik) in a hotel. Clearly this is not a wise move, but in case we weren't aware of that fact we're given jarring cuts to images of a mouse approaching a trap and of animals on the savanna sussing out their safety.

These juxtapositions are just an inkling of what's to come, as we'll later get full blasts of Koyaanisqatsi-esque montage – ranging from dinosaurs to busy urban centers to rhinos making love. These images mostly come as Professor Norman (Morgan Freeman) gives a lecture about what would happen if a human had access to higher percentages of their brain, which just so happens to describe what is happening to Lucy at that very moment.

Lucy, you see, has been made an inadvertent mule for a new narcotic. One Mr Keng's baddies get a hold of her, she's knocked out and gets “CPH4” inserted in her belly. It's a bag of crystals that kinda look like a blue version of the fancy overpriced salt you've always wanted to buy from Dean & DeLuca. When some would-be molesters end up beating her, the substance leaks into her blood stream and – boom – a new superhero is born.

The first two-thirds of this 90-minute film are propulsive and fun. Lucy is driven to a little vengeance, but is also on the hunt for the other bags of the drugs. You see, CPH4 is a naturally occurring substance during pregnancy. (It's what helps our bones grow, says a character who may as well be named Dr Exposition.) Since Lucy has mainlined the stuff, her brain power is now escalating from the typical 10%, and with it comes all sorts of magical powers. She can manipulate phone lines, make people levitate, and type at supersonic speeds. But she also knows that she'll only survive for a few more hours. (How does she know this? She's using a larger percentage of her brain! She knows things!) She'll need the additional crystals to reach the full 100% and “transcend” and, hopefully, give Freeman the knowledge that humankind seeks.

The end of the movie goes completely off the rails, but in a way that is charming in its stupidity. It's like 2001: A Space Odyssey for those with short attention spans, and those people need to have their minds blown, too, I suppose. Unfortunately, when Lucy heads toward her psychedelic freakout and the screenplay's stakes are raised, there's a piece of action with Korean baddies fighting French cops that's completely worthless. Basically, anything that isn't Scarlett besting martial artists with telekinesis or penetrating time and space with her glowering eyes just dies on the screen.

That the action comes to Besson's native France is marvelous, as it affords the film a rather messy car chase through the First Arrondissement. Johansson interrupts the action with vague philosophical musings like “we never really die.” These blatant lowest common denominator moments mixed with a twinge of deep meaning is, I feel, the essence du Besson.

It isn't saying much, given what he's been up to lately, but it's fair to call this his finest work since The Fifth Element. Some in the audience will hiss “huh?” as the film fades to black, but I'll argue that the preposterous conclusion (oh, just wait until you see what Morgan Freeman is left holding in the last scene) represents a genuine auteur leaving us with his pure sentiments. I can't imagine that Besson actually believes this movie makes sense, but there's an authenticity to his overreaching that adds a sparkle not seen in typical comic-book movie fare. Even with only 10% of my brain I can see that while this movie isn't what I'd typically call good, it is, undeniably, enjoyable mindlessness.

• Lucy opens in the US on 25 July, Australia on 31 July and the UK on 22 August